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Aperture Area Calculator

Calculate Snell's law refraction, critical angles, lens maker focal length, magnification, diffraction grating, and laser beam spot size for aperture area.

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Input Optical Parameters

Enter refractive indices, focal length, or incident angle.

Refracted Angle θ₂ / Critical Angle

27.73 degrees
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Snell's Law of Refraction

Light bends toward the normal when entering a denser medium (n₂ > n₁): n₁ × sin(θ₁) = n₂ × sin(θ₂). Speed of light in vacuum c = 299,792,458 m/s.

Calculation Methodology & Details

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Formula

Snell's Law: n₁ sin(θ₁) = n₂ sin(θ₂) Critical Angle: θ_c = arcsin(n₂ / n₁) for n₁ > n₂ Thin Lens Equation: 1/f = 1/d_o + 1/d_i Lens Power: P = 1 / f (Diopters)

Applies geometric ray optics, wave diffraction interference, lens maker curvature equations, and optical fiber total internal reflection.

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Important Disclaimer

Calculations assume paraxial thin lens approximations and isotropic homogeneous media unless non-linear optical dispersion is specified.

How to Calculate Step-by-Step

Follow these steps to complete the calculation:

1

Step 1

Select medium refractive indices (Air n=1.00, Water n=1.33, Glass n=1.52, Diamond n=2.42).

2

Step 2

Input incident ray angle θ₁ (degrees) or object distance d_o and focal length f (mm).

3

Step 3

View refracted angle θ₂, critical angle θ_c for TIR, image distance d_i, optical power in Diopters (D), or angular resolution limit (arcsec).

Detailed Insights & Expert Guide

ℹ️ About this Calculation

The Aperture Area Calculator solves geometric optics ray paths, thin lens equations, telescope magnification, Rayleigh diffraction limits, Brewster polarizing angle, and optical fiber total internal reflection.

Variable Glossary

Input

Refractive Index (n)

Ratio of speed of light in vacuum c to phase velocity v in the material (n = c / v).

Parameter

Diopter Power (D)

Reciprocal of lens focal length measured in meters (D = 1 / f).

FAQ

When does Total Internal Reflection (TIR) occur?
TIR occurs when light travels from a higher refractive index medium (n₁) to a lower refractive index medium (n₂) at an incident angle exceeding the critical angle θ_c = arcsin(n₂ / n₁). 100% of light is reflected back.
What is the Rayleigh Criterion for angular resolution?
The Rayleigh Criterion defines the minimum angular separation θ = 1.22 × (λ / D) radians between two point sources where their Airy diffraction disks can still be resolved by a circular aperture of diameter D.
How is telescope magnification calculated?
Telescope Magnification M = Focal Length of Objective Lens (f_obj) / Focal Length of Eyepiece (f_eye). For example, a 1000mm objective with a 10mm eyepiece gives 100x magnification.